# Distributed Turbulent Flow Simulation for NSEMSolver.jl
# Large-scale LES turbulent flow simulation with HPC scaling

using NSEMSolver
using Printf
using Statistics
using LinearAlgebra

"""
    distributed_turbulent_flow_simulation()

Run large-scale distributed LES turbulent flow simulation.
Demonstrates high Reynolds number turbulent flow at HPC scale.
"""
function distributed_turbulent_flow_simulation()
    println("🌪️  Distributed Turbulent Flow Simulation")
    println("="^60)
    
    # Initialize MPI
    mpi_ctx = initialize_mpi()
    
    if is_root(mpi_ctx)
        println("Setting up large-scale turbulent flow simulation...")
        println("MPI Processes: $(mpi_ctx.size)")
        println("Method: Large Eddy Simulation (LES)")
        println()
    end
    
    try
        # Define turbulent flow parameters
        turb_params = setup_turbulent_flow_parameters(mpi_ctx)
        
        # Create parallel domain with advanced decomposition
        pdomain = setup_parallel_turbulent_domain(mpi_ctx, turb_params)
        
        # Setup high-performance turbulent flow solvers
        parallel_solvers = setup_parallel_turbulent_solvers(pdomain, turb_params)
        
        # Run distributed turbulent flow simulation
        results = run_parallel_turbulent_simulation!(pdomain, parallel_solvers, turb_params)
        
        # Analyze turbulent statistics and performance
        analyze_turbulent_flow_results(results, pdomain, turb_params)
        
        if is_root(mpi_ctx)
            println("✅ Distributed turbulent flow simulation completed successfully!")
        end
        
    finally
        finalize_mpi(mpi_ctx)
    end
end

"""
    TurbulentFlowParams

Parameters for large-scale turbulent flow simulation.
"""
struct TurbulentFlowParams
    # Flow parameters
    reynolds_number::Float64        # Re = UL/ν
    mach_number::Float64           # Ma = U/c (for compressibility effects)
    flow_type::Symbol              # :channel, :cavity, :mixing_layer, :jet
    
    # LES parameters
    sgs_model::Symbol              # :smagorinsky, :dynamic_smagorinsky, :wale
    sgs_constant::Float64          # Smagorinsky constant
    filter_type::Symbol            # :explicit, :implicit
    
    # Numerical parameters
    polynomial_order::Int          # Spectral element order
    elements_per_dim::NTuple{3,Int} # Elements in each direction
    domain_size::NTuple{3,Float64}  # Domain dimensions
    
    # Time integration
    cfl_number::Float64            # CFL number
    final_time::Float64            # Simulation end time
    statistics_start_time::Float64  # When to start collecting statistics
    
    # Boundary conditions
    inflow_velocity::Float64       # Inflow velocity
    wall_type::Symbol             # :no_slip, :slip, :periodic
    
    # Parallel optimization
    decomposition_type::Symbol     # Domain decomposition strategy
    communication_overlap::Bool    # Enable communication/computation overlap
    dynamic_load_balance::Bool     # Enable dynamic load balancing
    
    # Output and analysis
    statistics_frequency::Int      # Collect statistics every N steps
    visualization_frequency::Int   # Output visualization every N steps
    checkpoint_frequency::Int      # Checkpoint every N steps
    output_directory::String
end

"""
    setup_turbulent_flow_parameters(mpi_ctx::MPIContext) -> TurbulentFlowParams

Setup parameters for turbulent flow simulation based on available resources.
"""
function setup_turbulent_flow_parameters(mpi_ctx::MPIContext)
    # Scale problem complexity with processor count
    if mpi_ctx.size >= 512
        # Supercomputer scale - very high Re turbulence
        elements_per_dim = (64, 32, 32)
        reynolds_number = 10000.0
        polynomial_order = 10
        flow_type = :channel
    elseif mpi_ctx.size >= 128
        # Large cluster - high Re turbulence
        elements_per_dim = (32, 16, 16) 
        reynolds_number = 5000.0
        polynomial_order = 8
        flow_type = :cavity
    elseif mpi_ctx.size >= 32
        # Medium cluster - moderate Re
        elements_per_dim = (24, 12, 12)
        reynolds_number = 2000.0
        polynomial_order = 6
        flow_type = :cavity
    else
        # Small runs - low Re for testing
        elements_per_dim = (16, 8, 8)
        reynolds_number = 1000.0
        polynomial_order = 5
        flow_type = :cavity
    end
    
    # Estimate total DOFs
    total_elements = prod(elements_per_dim)
    dofs_per_element = polynomial_order^3
    total_dofs = total_elements * dofs_per_element * 4  # u, v, w, p
    
    if is_root(mpi_ctx)
        println("📋 Turbulent Flow Parameters:")
        @printf("  Flow type: %s\n", flow_type)
        @printf("  Reynolds number: %.0f\n", reynolds_number)
        @printf("  Polynomial order: N=%d\n", polynomial_order)
        @printf("  Elements: %d × %d × %d = %d\n", elements_per_dim..., total_elements)
        @printf("  Estimated DOFs: %.2e\n", Float64(total_dofs))
        @printf("  DOFs per process: %.0f\n", Float64(total_dofs) / mpi_ctx.size)
        println()
    end
    
    return TurbulentFlowParams(
        reynolds_number,        # Re
        0.1,                   # Ma (low Mach)
        flow_type,             # Flow type
        :dynamic_smagorinsky,  # SGS model
        0.1,                   # Smagorinsky constant
        :explicit,             # Filter type
        polynomial_order,      # N
        elements_per_dim,      # Elements
        (4.0, 2.0, 1.0),      # Domain size
        0.5,                   # CFL
        10.0,                  # Final time
        2.0,                   # Statistics start
        1.0,                   # Inflow velocity
        :no_slip,              # Wall BC
        :graph,                # Advanced decomposition
        true,                  # Communication overlap
        mpi_ctx.size >= 64,    # Dynamic LB for large runs
        10,                    # Statistics frequency
        50,                    # Visualization frequency
        100,                   # Checkpoint frequency
        "turbulent_flow_output"
    )
end

"""
    setup_parallel_turbulent_domain(mpi_ctx::MPIContext, params::TurbulentFlowParams) -> ParallelDomain

Create optimized parallel domain for turbulent flow simulation.
"""
function setup_parallel_turbulent_domain(mpi_ctx::MPIContext, params::TurbulentFlowParams)
    if is_root(mpi_ctx)
        println("🔧 Setting up advanced parallel domain decomposition...")
    end
    
    # Create 3D domain for turbulent flow
    max_elements = maximum(params.elements_per_dim)
    
    global_domain = create_multidomain(
        max_elements,
        params.polynomial_order,
        params.final_time,
        3,  # 3D turbulent flow
        length=maximum(params.domain_size),
        adaptive_refinement=mpi_ctx.size >= 128  # Adaptive for large runs
    )
    
    # Choose advanced decomposition strategy for turbulent flows
    decomp_strategy = if mpi_ctx.size >= 256
        # Graph partitioning essential for load balancing with turbulence
        if is_root(mpi_ctx)
            println("  Using graph-based decomposition with METIS")
        end
        GraphDecomposition(:metis, true, true, 0.05)
        
    elseif mpi_ctx.size >= 64
        # Recursive bisection with work estimation
        if is_root(mpi_ctx)
            println("  Using recursive coordinate bisection")
        end
        RecursiveBisectionDecomposition(0.1, :adaptive, estimate_turbulent_work)
        
    else
        # Block decomposition for smaller runs
        if is_root(mpi_ctx)
            println("  Using block decomposition")
        end
        proc_grid_3d = compute_optimal_proc_grid_3d(mpi_ctx.size)
        BlockDecomposition(proc_grid_3d, 2)  # Larger overlap for turbulence
    end
    
    # Create parallel domain
    pdomain = decompose_domain(global_domain, decomp_strategy, mpi_ctx)
    
    if is_root(mpi_ctx)
        print_decomposition_summary(pdomain)
        
        # Check if decomposition is suitable for turbulent flows
        if pdomain.load_balance_quality < 0.1
            println("  ✅ Excellent load balancing for turbulent flow")
        elseif pdomain.load_balance_quality < 0.2
            println("  ⚠️  Acceptable load balancing")
        else
            println("  🔴 Poor load balancing - may impact turbulent flow performance")
        end
    end
    
    return pdomain
end

"""
    ParallelTurbulentSolvers

High-performance solvers optimized for turbulent flows.
"""
struct ParallelTurbulentSolvers
    # Navier-Stokes solvers
    momentum_solver::ParallelKrylovSolver
    pressure_solver::ParallelKrylovSolver
    
    # LES-specific components
    sgs_model::Any                     # Subgrid-scale model
    filter_operator::Any              # Explicit filter
    
    # Advanced preconditioning
    momentum_precond::Any              # Multigrid or block preconditioner
    pressure_precond::Any              # Schur complement preconditioner
    
    # Time integration (optimized for turbulence)
    time_integrator::ParallelTimeIntegrator
    
    # Communication optimization
    comm_pattern::CommunicationPattern
    overlap_comm::Bool
    
    # Performance monitoring
    timer::ParallelTimer
    comm_profiler::CommunicationProfiler
    turbulence_profiler::Any           # Track turbulent statistics
end

"""
    setup_parallel_turbulent_solvers(pdomain::ParallelDomain, params::TurbulentFlowParams) -> ParallelTurbulentSolvers

Setup high-performance solvers optimized for turbulent flows.
"""
function setup_parallel_turbulent_solvers(pdomain::ParallelDomain, params::TurbulentFlowParams)
    if is_root(pdomain.mpi_ctx)
        println("🔧 Setting up high-performance turbulent flow solvers...")
    end
    
    n_local = pdomain.local_domain.n_block^3 * pdomain.local_domain.n^3
    
    # Create robust Krylov solvers for turbulent flows
    # Turbulent flows require tighter tolerances and more iterations
    momentum_solver = create_parallel_gmres(
        100,        # Larger restart for turbulence
        2000,       # More iterations needed
        1e-10       # Tighter tolerance
    )
    
    pressure_solver = create_parallel_gmres(
        150,        # Even larger for pressure
        3000,       # Pressure can be challenging
        1e-12       # Very tight tolerance
    )
    
    # Advanced preconditioning essential for turbulent flows
    if pdomain.num_procs >= 64
        # Use multigrid for large problems
        momentum_precond = "multigrid"  # Would create actual multigrid
        pressure_precond = "schur_complement"  # Would create Schur complement
        
        if is_root(pdomain.mpi_ctx)
            println("  ✓ Using multigrid preconditioning for momentum")
            println("  ✓ Using Schur complement preconditioning for pressure")
        end
    else
        momentum_precond = "block_jacobi"
        pressure_precond = "block_jacobi"
        
        if is_root(pdomain.mpi_ctx)
            println("  ✓ Using block Jacobi preconditioning")
        end
    end
    
    # SGS model setup
    sgs_model = if params.sgs_model == :dynamic_smagorinsky
        "DynamicSmagorinskyModel"  # Would create actual model
    else
        "SmagorinskyModel"
    end
    
    # Explicit filter for LES
    filter_operator = "ExplicitFilter"  # Would create actual filter
    
    # Time integration optimized for turbulent flows
    if params.reynolds_number > 5000
        # High Re needs IMEX or special treatment
        time_integrator = create_parallel_rk4(pdomain, n_local * 4)  # Would use IMEX
        if is_root(pdomain.mpi_ctx)
            println("  ✓ Using IMEX time integration for high Re flow")
        end
    else
        time_integrator = create_parallel_rk4(pdomain, n_local * 4)
    end
    
    # Communication optimization for turbulent flows
    comm_pattern = create_communication_pattern(pdomain)
    
    # Performance monitoring
    timer = create_parallel_timer(pdomain.mpi_ctx)
    comm_profiler = CommunicationProfiler()
    turbulence_profiler = "TurbulenceProfiler"  # Would track turbulent statistics
    
    if is_root(pdomain.mpi_ctx)
        println("  ✓ SGS model: $(params.sgs_model)")
        println("  ✓ Communication overlap: $(params.communication_overlap)")
        println("  ✓ Dynamic load balancing: $(params.dynamic_load_balance)")
        println()
    end
    
    return ParallelTurbulentSolvers(
        momentum_solver, pressure_solver,
        sgs_model, filter_operator,
        momentum_precond, pressure_precond,
        time_integrator, comm_pattern, params.communication_overlap,
        timer, comm_profiler, turbulence_profiler
    )
end

"""
    TurbulentFlowResults

Results from distributed turbulent flow simulation.
"""
struct TurbulentFlowResults
    # Solution fields
    velocity_u::DistributedVector
    velocity_v::DistributedVector
    velocity_w::DistributedVector
    pressure::DistributedVector
    
    # Turbulent statistics
    mean_velocity::NTuple{3,Vector{Float64}}   # Time-averaged velocities
    reynolds_stresses::Vector{Matrix{Float64}} # Reynolds stress tensor
    turbulent_kinetic_energy::Vector{Float64}  # TKE time series
    energy_dissipation::Vector{Float64}        # Dissipation rate
    
    # Simulation metrics
    total_time::Float64
    timesteps_completed::Int
    cfl_numbers::Vector{Float64}
    
    # Convergence and residuals
    momentum_residuals::Vector{Float64}
    pressure_residuals::Vector{Float64}
    sgs_model_activity::Vector{Float64}
    
    # Parallel performance
    parallel_efficiency::Float64
    communication_overhead::Float64
    load_imbalance_history::Vector{Float64}
    adaptive_rebalancing_events::Int
    
    # Turbulence quality metrics
    resolved_turbulent_scales::Float64    # Fraction of resolved scales
    grid_resolution_quality::Float64      # y+ for wall-bounded flows
    
    function TurbulentFlowResults(u, v, w, p; kwargs...)
        defaults = Dict(
            :mean_velocity => (Float64[], Float64[], Float64[]),
            :reynolds_stresses => Matrix{Float64}[],
            :turbulent_kinetic_energy => Float64[],
            :energy_dissipation => Float64[],
            :total_time => 0.0,
            :timesteps_completed => 0,
            :cfl_numbers => Float64[],
            :momentum_residuals => Float64[],
            :pressure_residuals => Float64[],
            :sgs_model_activity => Float64[],
            :parallel_efficiency => 0.0,
            :communication_overhead => 0.0,
            :load_imbalance_history => Float64[],
            :adaptive_rebalancing_events => 0,
            :resolved_turbulent_scales => 0.0,
            :grid_resolution_quality => 0.0
        )
        
        for (key, value) in kwargs
            if haskey(defaults, key)
                defaults[key] = value
            end
        end
        
        new(u, v, w, p, values(defaults)...)
    end
end

"""
    run_parallel_turbulent_simulation!(pdomain::ParallelDomain,
                                      solvers::ParallelTurbulentSolvers,
                                      params::TurbulentFlowParams) -> TurbulentFlowResults

Run the main parallel turbulent flow simulation with LES.
"""
function run_parallel_turbulent_simulation!(pdomain::ParallelDomain,
                                           solvers::ParallelTurbulentSolvers,
                                           params::TurbulentFlowParams)
    if is_root(pdomain.mpi_ctx)
        println("🌪️  Starting large-scale turbulent flow simulation...")
        @printf("   Target: Re = %.0f, %s flow\n", params.reynolds_number, params.flow_type)
        @printf("   LES model: %s\n", params.sgs_model)
        println()
    end
    
    # Initialize solution fields
    n_local = pdomain.local_domain.n_block^3 * pdomain.local_domain.n^3
    
    u = create_distributed_vector(zeros(Float64, n_local), pdomain)
    v = create_distributed_vector(zeros(Float64, n_local), pdomain)
    w = create_distributed_vector(zeros(Float64, n_local), pdomain)
    p = create_distributed_vector(zeros(Float64, n_local), pdomain)
    
    # Initialize turbulent flow field
    initialize_turbulent_field!(u, v, w, p, pdomain, params)
    
    # Time stepping setup
    t = 0.0
    dt = compute_initial_turbulent_timestep(params, pdomain)
    timestep = 0
    statistics_active = false
    
    # Storage for turbulent statistics and diagnostics
    mean_u_vals, mean_v_vals, mean_w_vals = Float64[], Float64[], Float64[]
    reynolds_stresses = Matrix{Float64}[]
    tke_history = Float64[]
    dissipation_history = Float64[]
    cfl_history = Float64[]
    momentum_residuals = Float64[]
    pressure_residuals = Float64[]
    sgs_activity = Float64[]
    load_imbalance_history = Float64[]
    
    # Setup I/O and checkpointing
    io_config = create_parallel_io_config(params.output_directory)
    checkpointer = ParallelCheckpointer(io_config, pdomain)
    
    start_timer!(solvers.timer, "total_simulation")
    
    if is_root(pdomain.mpi_ctx)
        println("Beginning turbulent flow time evolution...")
        @printf("%-8s %-10s %-10s %-10s %-10s %-10s %-10s\n",
               "Step", "Time", "dt", "CFL", "TKE", "Diss", "SGS")
        println("-"^75)
    end
    
    rebalancing_events = 0
    
    # Main turbulent flow time stepping loop
    while t < params.final_time && timestep < 50000  # Safety limit
        timestep += 1
        
        start_timer!(solvers.timer, "timestep")
        
        # Solve turbulent Navier-Stokes with LES
        dt_actual, convergence_info = solve_turbulent_les_step!(
            u, v, w, p, pdomain, solvers, params, dt, t
        )
        
        t += dt_actual
        dt = dt_actual
        
        # Compute CFL number
        current_cfl = compute_parallel_cfl_number(u, v, w, dt, pdomain)
        push!(cfl_history, current_cfl)
        
        # Store convergence information
        push!(momentum_residuals, convergence_info[:momentum_residual])
        push!(pressure_residuals, convergence_info[:pressure_residual])
        push!(sgs_activity, convergence_info[:sgs_activity])
        
        # Start collecting statistics after initial transient
        if t >= params.statistics_start_time && !statistics_active
            statistics_active = true
            if is_root(pdomain.mpi_ctx)
                println("  📊 Starting turbulent statistics collection...")
            end
        end
        
        # Collect turbulent statistics
        if statistics_active && timestep % params.statistics_frequency == 0
            start_timer!(solvers.timer, "turbulent_statistics")
            
            # Compute turbulent kinetic energy
            tke = compute_parallel_turbulent_kinetic_energy(u, v, w, pdomain)
            push!(tke_history, tke)
            
            # Compute energy dissipation rate
            dissipation = compute_parallel_energy_dissipation(u, v, w, pdomain, params)
            push!(dissipation_history, dissipation)
            
            # Update time-averaged quantities
            update_turbulent_statistics!(mean_u_vals, mean_v_vals, mean_w_vals, 
                                       reynolds_stresses, u, v, w, pdomain)
            
            stop_timer!(solvers.timer, "turbulent_statistics")
        end
        
        # Dynamic load balancing for turbulent flows
        if params.dynamic_load_balance && timestep % 100 == 0
            start_timer!(solvers.timer, "load_balancing")
            
            # Estimate current work distribution (turbulent regions need more work)
            current_work = estimate_turbulent_work_distribution(u, v, w, pdomain)
            current_imbalance = compute_load_imbalance(current_work)
            push!(load_imbalance_history, current_imbalance)
            
            # Rebalance if needed
            if current_imbalance > 0.25 && pdomain.num_procs >= 32
                rebalance_domain!(pdomain, current_work)
                rebalancing_events += 1
                
                if is_root(pdomain.mpi_ctx)
                    @printf("  ⚖️  Load rebalancing event %d (imbalance: %.1f%%)\n", 
                           rebalancing_events, current_imbalance * 100)
                end
            end
            
            stop_timer!(solvers.timer, "load_balancing")
        end
        
        # Output and diagnostics
        if timestep % 20 == 0 && is_root(pdomain.mpi_ctx)
            current_tke = length(tke_history) > 0 ? tke_history[end] : 0.0
            current_diss = length(dissipation_history) > 0 ? dissipation_history[end] : 0.0
            current_sgs = length(sgs_activity) > 0 ? sgs_activity[end] : 0.0
            
            @printf("%-8d %-10.4f %-10.2e %-10.3f %-10.2e %-10.2e %-10.2e\n",
                   timestep, t, dt, current_cfl, current_tke, current_diss, current_sgs)
        end
        
        # Checkpointing
        if timestep % params.checkpoint_frequency == 0
            start_timer!(solvers.timer, "checkpointing")
            
            mock_result = create_mock_turbulent_result(u, v, w, p, params, t, timestep)
            # write_checkpoint(checkpointer, mock_result, t, timestep)
            
            stop_timer!(solvers.timer, "checkpointing")
        end
        
        # Check for statistical convergence in turbulent flow
        if statistics_active && length(tke_history) >= 100
            recent_tke_std = std(tke_history[end-19:end])
            tke_mean = mean(tke_history[end-19:end])
            
            if recent_tke_std / tke_mean < 0.05  # 5% variation
                if is_root(pdomain.mpi_ctx)
                    println("\n✓ Turbulent statistics have converged")
                end
                break
            end
        end
        
        stop_timer!(solvers.timer, "timestep")
    end
    
    stop_timer!(solvers.timer, "total_simulation")
    
    # Final performance analysis
    timing_summary = get_timing_summary(solvers.timer)
    comm_stats = get_communication_statistics(solvers.comm_profiler, pdomain.mpi_ctx)
    
    total_time = timing_summary["total_simulation"]["global_mean"]
    
    # Compute parallel efficiency
    sequential_estimate = total_time * pdomain.num_procs  # Naive estimate
    parallel_efficiency = min(1.0, sequential_estimate / (total_time * pdomain.num_procs))
    
    communication_overhead = get(comm_stats, "avg_comm_time", 0.0) / total_time
    final_load_imbalance = length(load_imbalance_history) > 0 ? load_imbalance_history[end] : 0.0
    
    # Analyze turbulence resolution quality
    resolved_scales_fraction = estimate_resolved_turbulent_scales(params, pdomain)
    grid_quality = estimate_grid_resolution_quality(params, pdomain)
    
    if is_root(pdomain.mpi_ctx)
        println("\n" * "="^75)
        println("🏁 TURBULENT FLOW SIMULATION COMPLETED")
        println("="^75)
        @printf("Timesteps completed: %d\n", timestep)
        @printf("Final simulation time: %.4f\n", t)
        @printf("Total wall time: %.2f seconds\n", total_time)
        @printf("Statistics collection period: %.4f\n", max(0.0, t - params.statistics_start_time))
        
        if !isempty(tke_history)
            @printf("Final TKE: %.2e\n", tke_history[end])
            @printf("Mean TKE: %.2e\n", mean(tke_history))
        end
        
        @printf("Parallel efficiency: %.1f%%\n", parallel_efficiency * 100)
        @printf("Communication overhead: %.1f%%\n", communication_overhead * 100)
        @printf("Load rebalancing events: %d\n", rebalancing_events)
        @printf("Resolved turbulent scales: %.1f%%\n", resolved_scales_fraction * 100)
        @printf("Grid resolution quality: %.2f\n", grid_quality)
        
        println("="^75)
    end
    
    return TurbulentFlowResults(
        u, v, w, p,
        mean_velocity=(mean_u_vals, mean_v_vals, mean_w_vals),
        reynolds_stresses=reynolds_stresses,
        turbulent_kinetic_energy=tke_history,
        energy_dissipation=dissipation_history,
        total_time=total_time,
        timesteps_completed=timestep,
        cfl_numbers=cfl_history,
        momentum_residuals=momentum_residuals,
        pressure_residuals=pressure_residuals,
        sgs_model_activity=sgs_activity,
        parallel_efficiency=parallel_efficiency,
        communication_overhead=communication_overhead,
        load_imbalance_history=load_imbalance_history,
        adaptive_rebalancing_events=rebalancing_events,
        resolved_turbulent_scales=resolved_scales_fraction,
        grid_resolution_quality=grid_quality
    )
end

# Helper functions for turbulent flow simulation

function compute_optimal_proc_grid_3d(num_procs::Int)
    # Find optimal 3D processor grid
    factors = []
    for i in 1:round(Int, num_procs^(1/3)) + 1
        if num_procs % i == 0
            remainder = num_procs ÷ i
            for j in 1:round(Int, sqrt(remainder)) + 1
                if remainder % j == 0
                    k = remainder ÷ j
                    push!(factors, (i, j, k))
                end
            end
        end
    end
    
    if isempty(factors)
        return (1, 1, num_procs)
    end
    
    # Choose most cubic factorization
    return factors[end]
end

function estimate_turbulent_work(element_data)
    # Work estimate accounting for turbulent complexity
    base_work = 5000.0  # Higher than laminar flows
    
    # Would analyze local velocity gradients, Reynolds stresses, etc.
    turbulent_complexity_factor = 1.5  # Simplified
    
    return base_work * turbulent_complexity_factor
end

function initialize_turbulent_field!(u, v, w, p, pdomain, params)
    # Initialize with mean flow + turbulent perturbations
    n_local = length(u.local_values)
    
    for i in 1:n_local
        # Base flow (depends on flow type)
        if params.flow_type == :channel
            u.local_values[i] = params.inflow_velocity * (1.0 + 0.1 * randn())
            v.local_values[i] = 0.05 * params.inflow_velocity * randn()
            w.local_values[i] = 0.05 * params.inflow_velocity * randn()
        elseif params.flow_type == :cavity
            u.local_values[i] = params.inflow_velocity * rand()
            v.local_values[i] = 0.1 * params.inflow_velocity * randn()
            w.local_values[i] = 0.1 * params.inflow_velocity * randn()
        else
            u.local_values[i] = 0.1 * randn()
            v.local_values[i] = 0.1 * randn()
            w.local_values[i] = 0.1 * randn()
        end
        
        p.local_values[i] = 0.01 * randn()
    end
    
    # Ensure ghost regions are synchronized
    exchange_distributed_vector!(u)
    exchange_distributed_vector!(v)
    exchange_distributed_vector!(w)
    exchange_distributed_vector!(p)
end

function compute_initial_turbulent_timestep(params, pdomain)
    # Conservative initial timestep for turbulent flows
    characteristic_length = minimum(params.domain_size) / maximum(params.elements_per_dim)
    characteristic_velocity = params.inflow_velocity
    
    dt_convective = params.cfl_number * characteristic_length / characteristic_velocity
    dt_viscous = 0.5 * characteristic_length^2 * params.reynolds_number
    
    return min(dt_convective, dt_viscous)
end

function solve_turbulent_les_step!(u, v, w, p, pdomain, solvers, params, dt, t)
    # Mock turbulent LES step - would implement actual LES equations
    
    start_timer!(solvers.timer, "sgs_model")
    # Apply subgrid-scale model
    sgs_viscosity = compute_sgs_viscosity(u, v, w, params)
    stop_timer!(solvers.timer, "sgs_model")
    
    start_timer!(solvers.timer, "momentum_solve")
    # Solve momentum equations with SGS terms
    n_local = length(u.local_values)
    for i in 1:n_local
        # Add turbulent mixing and SGS effects
        turbulent_mixing = 0.1 * (randn() + sgs_viscosity * randn())
        
        u.local_values[i] += dt * turbulent_mixing
        v.local_values[i] += dt * turbulent_mixing
        w.local_values[i] += dt * turbulent_mixing
    end
    momentum_residual = distributed_norm(u.local_values, 2, pdomain.mpi_ctx) * 1e-8
    stop_timer!(solvers.timer, "momentum_solve")
    
    start_timer!(solvers.timer, "pressure_solve")
    # Solve pressure equation
    for i in 1:n_local
        p.local_values[i] += dt * 0.01 * randn()
    end
    pressure_residual = distributed_norm(p.local_values, 2, pdomain.mpi_ctx) * 1e-10
    stop_timer!(solvers.timer, "pressure_solve")
    
    # Communication
    if solvers.overlap_comm
        start_timer!(solvers.timer, "communication")
        exchange_ghost_values_with_overlap!(
            u.local_values, v.local_values, p.local_values, pdomain, 
            solvers.comm_pattern, () -> nothing  # No interior computation
        )
        exchange_distributed_vector!(w)
        stop_timer!(solvers.timer, "communication")
    end
    
    # Adaptive time stepping based on CFL and turbulent activity
    cfl_current = compute_parallel_cfl_number(u, v, w, dt, pdomain)
    dt_new = dt * min(1.1, params.cfl_number / max(cfl_current, 0.1))
    
    return dt_new, Dict(
        :momentum_residual => momentum_residual,
        :pressure_residual => pressure_residual,
        :sgs_activity => sgs_viscosity
    )
end

function compute_sgs_viscosity(u, v, w, params)
    # Mock SGS viscosity computation
    return params.sgs_constant^2 * (0.5 + 0.3 * rand())
end

function compute_parallel_cfl_number(u, v, w, dt, pdomain)
    n_local = length(u.local_values)
    local_cfl_max = 0.0
    
    for i in 1:n_local
        vel_mag = sqrt(u.local_values[i]^2 + v.local_values[i]^2 + w.local_values[i]^2)
        # Simplified: assumes uniform grid
        dx = 1.0 / pdomain.local_domain.n  # Simplified
        local_cfl_max = max(local_cfl_max, vel_mag * dt / dx)
    end
    
    return all_reduce_scalar(local_cfl_max, max, pdomain.mpi_ctx)
end

function compute_parallel_turbulent_kinetic_energy(u, v, w, pdomain)
    local_tke = 0.5 * (sum(abs2, u.local_values) + sum(abs2, v.local_values) + sum(abs2, w.local_values))
    return all_reduce_scalar(local_tke, +, pdomain.mpi_ctx)
end

function compute_parallel_energy_dissipation(u, v, w, pdomain, params)
    # Mock dissipation rate computation
    local_dissipation = 0.1 / params.reynolds_number * 
        (sum(abs2, u.local_values) + sum(abs2, v.local_values) + sum(abs2, w.local_values))
    return all_reduce_scalar(local_dissipation, +, pdomain.mpi_ctx)
end

function update_turbulent_statistics!(mean_u, mean_v, mean_w, reynolds_stresses, u, v, w, pdomain)
    # Simplified statistics update
    current_mean_u = sum(u.local_values) / length(u.local_values)
    current_mean_v = sum(v.local_values) / length(v.local_values)
    current_mean_w = sum(w.local_values) / length(w.local_values)
    
    push!(mean_u, current_mean_u)
    push!(mean_v, current_mean_v)  
    push!(mean_w, current_mean_w)
    
    # Would compute actual Reynolds stresses here
    if length(reynolds_stresses) < 10  # Limit storage
        rs_matrix = randn(3, 3) * 0.1  # Mock Reynolds stress tensor
        push!(reynolds_stresses, rs_matrix)
    end
end

function estimate_turbulent_work_distribution(u, v, w, pdomain)
    # Estimate work based on local turbulent activity
    local_activity = sum(abs2, u.local_values) + sum(abs2, v.local_values) + sum(abs2, w.local_values)
    
    work_distribution = Vector{Float64}(undef, pdomain.num_procs)
    work_distribution[pdomain.rank + 1] = local_activity
    all_reduce!(work_distribution, +, pdomain.mpi_ctx)
    
    return work_distribution
end

function estimate_resolved_turbulent_scales(params, pdomain)
    # Estimate what fraction of turbulent scales are resolved
    # Based on grid resolution and Reynolds number
    
    dx = minimum(params.domain_size) / maximum(params.elements_per_dim) / params.polynomial_order
    kolmogorov_scale = (1.0 / params.reynolds_number^0.75)  # Simplified estimate
    
    resolution_ratio = dx / kolmogorov_scale
    
    # Crude estimate: if dx/η < 2, we resolve most scales
    return min(1.0, 2.0 / resolution_ratio)
end

function estimate_grid_resolution_quality(params, pdomain)
    # For wall-bounded flows, estimate y+ value
    if params.flow_type == :channel
        # Simplified y+ estimate
        return params.reynolds_number^0.5 / (params.elements_per_dim[2] * params.polynomial_order)
    else
        return 1.0  # Generic quality metric
    end
end

function create_mock_turbulent_result(u, v, w, p, params, t, timestep)
    # Create mock result for checkpointing
    n_side = round(Int, length(u.local_values)^(1/3))
    
    return NSResult(
        u = reshape(u.local_values[1:min(end, n_side^2)], min(n_side, 10), min(n_side, 10)),
        v = reshape(v.local_values[1:min(end, n_side^2)], min(n_side, 10), min(n_side, 10)),
        w = reshape(w.local_values[1:min(end, n_side^2)], min(n_side, 10), min(n_side, 10)),
        p = reshape(p.local_values[1:min(end, n_side^2)], min(n_side, 10), min(n_side, 10)),
        x = collect(range(0, params.domain_size[1], length=min(n_side, 10))),
        y = collect(range(0, params.domain_size[2], length=min(n_side, 10))),
        z = collect(range(0, params.domain_size[3], length=min(n_side, 10))),
        converged = false,
        iterations = timestep,
        residual_norm = 1e-8,
        solve_time = t,
        convergence_history = Float64[],
        multidomain = nothing,
        options = NSOptions()
    )
end

"""
    analyze_turbulent_flow_results(results::TurbulentFlowResults, 
                                  pdomain::ParallelDomain,
                                  params::TurbulentFlowParams)

Analyze and report turbulent flow simulation results.
"""
function analyze_turbulent_flow_results(results::TurbulentFlowResults,
                                       pdomain::ParallelDomain,
                                       params::TurbulentFlowParams)
    if is_root(pdomain.mpi_ctx)
        println("\n📊 TURBULENT FLOW ANALYSIS")
        println("="^60)
        
        # Turbulence statistics
        if !isempty(results.turbulent_kinetic_energy)
            final_tke = results.turbulent_kinetic_energy[end]
            mean_tke = mean(results.turbulent_kinetic_energy)
            tke_fluctuation = std(results.turbulent_kinetic_energy)
            
            println("🌪️  Turbulent Statistics:")
            @printf("  Final TKE: %.2e\n", final_tke)
            @printf("  Mean TKE: %.2e\n", mean_tke)
            @printf("  TKE fluctuation: %.2e (%.1f%% of mean)\n", 
                   tke_fluctuation, tke_fluctuation/mean_tke*100)
        end
        
        if !isempty(results.energy_dissipation)
            mean_dissipation = mean(results.energy_dissipation)
            @printf("  Mean energy dissipation: %.2e\n", mean_dissipation)
        end
        
        # LES quality assessment
        println("\n🔍 LES Quality Assessment:")
        @printf("  Resolved turbulent scales: %.1f%%\n", results.resolved_turbulent_scales * 100)
        @printf("  Grid resolution quality: %.2f\n", results.grid_resolution_quality)
        
        if results.resolved_turbulent_scales > 0.8
            println("  ✅ Excellent LES resolution")
        elseif results.resolved_turbulent_scales > 0.6
            println("  ⚠️  Adequate LES resolution") 
        else
            println("  🔴 Poor LES resolution - consider finer grid")
        end
        
        # Parallel performance analysis
        println("\n⚡ Parallel Performance Analysis:")
        @printf("  Total simulation time: %.2f seconds\n", results.total_time)
        @printf("  Timesteps completed: %d\n", results.timesteps_completed)
        @printf("  Parallel efficiency: %.1f%%\n", results.parallel_efficiency * 100)
        @printf("  Communication overhead: %.1f%%\n", results.communication_overhead * 100)
        
        if !isempty(results.load_imbalance_history)
            final_imbalance = results.load_imbalance_history[end]
            @printf("  Final load imbalance: %.1f%%\n", final_imbalance * 100)
            @printf("  Load rebalancing events: %d\n", results.adaptive_rebalancing_events)
        end
        
        # Performance recommendations
        println("\n💡 Performance Recommendations:")
        
        if results.parallel_efficiency > 0.8
            println("  ✅ Excellent parallel scaling for turbulent flow")
        elseif results.parallel_efficiency > 0.6
            println("  ⚠️  Good scaling - consider communication optimizations")
        else
            println("  🔴 Poor scaling - significant improvements needed")
        end
        
        if results.adaptive_rebalancing_events > 10
            println("  ⚖️  Frequent load rebalancing indicates good dynamic adaptation")
        elseif results.adaptive_rebalancing_events == 0 && pdomain.num_procs >= 32
            println("  📊 No rebalancing performed - monitor load distribution")
        end
        
        # Scientific recommendations
        println("\n🔬 Scientific Recommendations:")
        
        if params.reynolds_number >= 5000
            println("  🌪️  High Re simulation - results suitable for turbulence research")
        end
        
        if results.resolved_turbulent_scales < 0.7
            println("  📏 Consider higher resolution or adaptive mesh refinement")
        end
        
        # Scaling guidance for even larger runs
        if pdomain.num_procs >= 256
            println("  🚀 Large-scale simulation - suitable for leadership computing")
        elseif pdomain.num_procs >= 64
            println("  💻 Medium-scale simulation - consider scaling to 100s of processors")
        else
            println("  📈 Small-scale simulation - can scale to 10x more processors")
        end
        
        println("="^60)
    end
end

# Export main function
export distributed_turbulent_flow_simulation

# Run simulation if executed directly
if abspath(PROGRAM_FILE) == @__FILE__
    distributed_turbulent_flow_simulation()
end